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» On the Turing Degrees of Divergence Bounded Computable Reals
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MFCS
2009
Springer
15 years 2 months ago
Time-Bounded Kolmogorov Complexity and Solovay Functions
Abstract. A Solovay function is a computable upper bound g for prefixfree Kolmogorov complexity K that is nontrivial in the sense that g agrees with K, up to some additive constan...
Rupert Hölzl, Thorsten Kräling, Wolfgang...
COCOON
2005
Springer
14 years 11 months ago
Solovay Reducibility on D-c.e Real Numbers
A c.e. real x is Solovay reducible to another c.e. real y if x can be approximated at least as efficiently as y by means of increasing computable sequences of rational numbers. The...
Robert Rettinger, Xizhong Zheng
CORR
2010
Springer
111views Education» more  CORR 2010»
14 years 10 months ago
Improved complexity bounds for real root isolation using Continued Fractions
We consider the problem of isolating the real roots of a square-free polynomial with integer coefficients using (variants of) the continued fraction algorithm (CF). We introduce a...
Elias P. Tsigaridas
COLT
1993
Springer
15 years 2 months ago
Bounding the Vapnik-Chervonenkis Dimension of Concept Classes Parameterized by Real Numbers
The Vapnik-Chervonenkis (V-C) dimension is an important combinatorial tool in the analysis of learning problems in the PAC framework. For polynomial learnability, we seek upper bou...
Paul W. Goldberg, Mark Jerrum
ESA
2006
Springer
147views Algorithms» more  ESA 2006»
15 years 1 months ago
Univariate Polynomial Real Root Isolation: Continued Fractions Revisited
We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algeb...
Elias P. Tsigaridas, Ioannis Z. Emiris